My game gets stuck loading at the main menu. It gets the whole way to "checking DLC," the last thing it has to do before it gives you control and it refuses to finish loading.

Do you have DLC installed ?
Did you delete them and try again to play ?
I have a friend who had the same problem. He deleted the DLC, loaded his game, played for awhile, saved his game, then downloaded again the DLC, and it worked.